Nonzero currents characterize the nonequilibrium state in stochastic dynamics (or master equation) models of natural systems. In such models there is a matrix $R$ of transition probabilities connecting the states of the system. We show that if the strength of a transition increases, so does the current along the corresponding bond. We also address the inverse problem: given a set of observed currents, we show the extent to which the original “$R$” can be recovered. These considerations lead to a general discussion of time scales and substance flows.

• Received 18 June 2008

DOI:https://doi.org/10.1103/PhysRevE.79.021112